W-Algebras, New Rational Models and Completeness of the c = 1 Classification

Details W-Algebras, New Rational Models and Completeness of the c = 1 Classification W-Algebras, New Rational Models and Completeness of the c = 1 Classification

1992-07-08

arxiv.org/abs/hep-th/9207019v1

Commun.Math.Phys. 157 (1993) 179-212

Physics

High Energy Physics

High Energy Physics - Theory

33 pages LaTeX, BONN-HE-92-08

Scientific paper

10.1007/BF02098024

Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If $c = 1 - 24k$, there exists a W(2,3k) algebra for k in $Z_{+}/2$ and a W(2,8k) algebra for k in $Z_{+}/4$. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these theories are rational. It is shown, that these non-unitary theories complete the classification of all rational theories with effective central charge $c_{eff} = 1$. The results are generalized to the case of extended supersymmetric conformal algebras.

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